Toeplitz operators on Dirichlet-Besov spaces

We study Toeplitz operators on the Besov spaces in the case of the open unit disk. We prove that a symbol satisfying a weak Lipschitz type condition induces a bounded Toeplitz operator. Such symbols do not need to be bounded functions or have continuous extensions to the boundary of the open unit disk. We discuss the problem of the existence of nontrivial compact Toeplitz operators, and also consider Fredholm properties and prove an index formula.

Schatten class Toeplitz operators on generalized Fock spaces

In this paper we characterize the Schatten p class membership of Toeplitz operators with positive measure symbols acting on generalized Fock spaces for the full range p>0.

Closed-loop feedback computation model of dynamical reputation based on the local trust evaluation in business-to-consumer e-commerce

Trust and reputation are important factors that influence the success of both traditional transactions in physical social networks and modern e-commerce in virtual Internet environments. It is difficult to define the concept of trust and quantify it because trust has both subjective and objective characteristics at the same time. A well-reported issue with reputation management system in business-to-consumer (BtoC) e-commerce is the “all good reputation” problem. In order to deal with the confusion, a new computational model of reputation is proposed in this paper. The ratings of each customer are set as basic trust score events. In addition, the time series of massive ratings are aggregated to formulate the sellers’ local temporal trust scores by Beta distribution. A logical model of trust and reputation is established based on the analysis of the dynamical relationship between trust and reputation. As for single goods with repeat transactions, an iterative mathematical model of trust and reputation is established with a closed-loop feedback mechanism. Numerical experiments on repeated transactions recorded over a period of 24 months are performed. The experimental results show that the proposed method plays guiding roles for both theoretical research into trust and reputation and the practical design of reputation systems in BtoC e-commerce.

Nox2 B-loop peptide, Nox2ds, specifically inhibits the NADPH oxidase Nox2

In recent years, reactive oxygen species (ROS) derived from the vascular isoforms of NADPH oxidase, Nox1, Nox2, and Nox4, have been implicated in many cardiovascular pathologies. As a result, the selective inhibition of these isoforms is an area of intense current investigation. In this study, we postulated that Nox2ds, a peptidic inhibitor that mimics a sequence in the cytosolic B-loop of Nox2, would inhibit ROS production by the Nox2-. but not the Noxl- and Nox4-oxidase systems. To test our hypothesis, the inhibitory activity of Nox2ds was assessed in cell-free assays using reconstituted systems expressing the Nox2-, canonical or hybrid Nox1- or Nox4-oxidase. Our findings demonstrate that Nox2ds, but not its scrambled control, potently inhibited superoxide (O(2)(center dot-)) production in the Nox2 cell-free system, as assessed by the cytochrome c assay. Electron paramagnetic resonance confirmed that Nox2ds inhibits O(2)(center dot-) production by Nox2 oxidase. In contrast, Nox2ds did not inhibit ROS production by either Nox1- or Nox4-oxidase. These findings demonstrate that Nox2ds is a selective inhibitor of Nox2-oxidase and support its utility to elucidate the role of Nox2 in organ pathophysiology and its potential as a therapeutic agent. (C) 2011 Elsevier Inc. All rights reserved.

Adhesion and protease activity in cell lines from human salivary gland tumors are regulated by the laminin-derived peptide AG73, syndecan-1 and beta 1 integrin

We studied the induction of protease activity by the laminin alpha 1-derived peptide AG73 in cells from adenoid cystic carcinoma (CAC2) and myoepithelioma (M1), respectively a malignant and a benign salivary gland tumors. Laminin alpha 1 chain and MMP9 were immunolocalized in adenoid cystic carcinoma and myoepithelioma in vivo and in vitro. Cells grown inside AG73-enriched laminin-111 exhibited large spaces in the extracellular matrix, suggestive of remodeling. The broad spectrum MMP inhibitor GM6001 decreased spaces induced by AG73 in CAC2 and M I cells. This result strongly suggests that AG73-mediated matrix remodeling involves matrix metalloproteinases. CAC2 and M1 cells cultured on AG73 showed a dose-dependent increase of MMP9 secretion, as detected by zymography. Furthermore, siRNA silencing of MMP9 decreased remodeling in 3D cultures. We searched for AG73 receptors regulating MMP9 activity in our cell lines. CAC2 and M1 cells grown on AG73 exhibited colocalization of syndecan-1 and beta 1 integrin. siRNA knockdown of syndecan-1 expression in these cells resulted in decreased adhesion to AG73 and reduced protease and remodeling activity. We investigated syndecan-1 co-receptors in both cell lines. Silencing beta 1 integrin inhibited adhesion to AG73, matrix remodeling and protease activity. Double-knockdown experiments were carried out to further explore syndecan-1 and beta 1 integrin cooperation. CAC2 cells transfected with both syndecan-1 and beta 1 integrin siRNA oligos showed significant decrease in adhesion to AG73. Simultaneous silencing of receptors also induced a decrease in protease activity. Our results suggest that syndecan-1 and beta 1 integrin signaling downstream of AG73 regulate adhesion and MMP production by CAC2 and M1 cells. (c) 2008 Elsevier B.V./International Society of Matrix Biology. All rights reserved.

Finite-dimensional global attractors in Banach spaces

We provide bounds on the upper box-counting dimension of negatively invariant subsets of Banach spaces, a problem that is easily reduced to covering the image of the unit ball under a linear map by a collection of balls of smaller radius. As an application of the abstract theory we show that the global attractors of a very broad class of parabolic partial differential equations (semilinear equations in Banach spaces) are finite-dimensional. (C) 2010 Elsevier Inc. All rights reserved.

The long wavelength limit of hard thermal loop effective actions

We derive a closed form expression for the long wavelength limit of the effective action for hard thermal loops in an external gravitational field. It is a function of the metric, independent of time derivatives. It is compared and contrasted with the static limit, and with the corresponding limits in an external Yang-Mills field. (C) 2009 Elsevier B.V. All rights reserved.

Magnetic hysteresis loop shift in NiFe(2)O(4) nanocrystalline powder with large grain boundary fraction

Magnetic properties of nanocrystalline NiFe(2)O(4) spinel mechanically processed for 350 h have been studied using temperature dependent from both zero-field and in-field (57)Fe Mossbauer spectrometry and magnetization measurements. The hyperfine structure allows us to distinguish two main magnetic contributions: one attributed to the crystalline grain core, which has magnetic properties similar to the NiFe(2)O(4) spinel-like structure (n-NiFe(2)O(4)) and the other one due to the disordered grain boundary region, which presents topological and chemical disorder features(d-NiFe(2)O(4)). Mossbauer spectrometry determines a large fraction for the d-NiFe(2)O(4) region(62% of total area) and also suggests a speromagnet-like structure for it. Under applied magnetic field, the n-NiFe(2)O(4) spins are canted with angle dependent on the applied field magnitude. Mossbauer data also show that even under 120 kOe no magnetic saturation is observed for the two magnetic phases. In addition, the hysteresis loops, recorded for scan field of 50 kOe, are shifted in both field and magnetization axes, for temperatures below about 50 K. The hysteresis loop shifts may be due to two main contributions: the exchange bias field at the d-NiFe(2)O(4)/n-NiFe(2)O(4) interfaces and the minor loop effect caused by a high magnetic anisotropy of the d-NiFe(2)O(4) phase. It has also been shown that the spin configuration of the spin-glass like phase is modified by the consecutive field cycles, consequently the n-NiFe(2)O(4)/d-NiFe(2)O(4) magnetic interaction is also affected in this process. (C) 2010 Elsevier B.V. All rights reserved.

Exact vortex solutions in a CP(N) Skyrme-Faddeev type model

We consider a four dimensional field theory with target space being CP(N) which constitutes a generalization of the usual Skyrme-Faddeev model defined on CP(1). We show that it possesses an integrable sector presenting an infinite number of local conservation laws, which are associated to the hidden symmetries of the zero curvature representation of the theory in loop space. We construct an infinite class of exact solutions for that integrable submodel where the fields are meromorphic functions of the combinations (x(1) + i x(2)) and (x(3) + x(0)) of the Cartesian coordinates of four dimensional Minkowski space-time. Among those solutions we have static vortices and also vortices with waves traveling along them with the speed of light. The energy per unity of length of the vortices show an interesting and intricate interaction among the vortices and waves.

The Hilbert space of the Chern-Simons theory on a cylinder: a loop quantum gravity approach

As a laboratory for loop quantum gravity, we consider the canonical quantization of the three-dimensional Chern-Simons theory on a noncompact space with the topology of a cylinder. Working within the loop quantization formalism, we define at the quantum level the constraints appearing in the canonical approach and completely solve them, thus constructing a gauge and diffeomorphism invariant physical Hilbert space for the theory. This space turns out to be infinite dimensional, but separable.

Proximal methods for nonlinear programming: double regularization and inexact subproblems

This paper describes the first phase of a project attempting to construct an efficient general-purpose nonlinear optimizer using an augmented Lagrangian outer loop with a relative error criterion, and an inner loop employing a state-of-the art conjugate gradient solver. The outer loop can also employ double regularized proximal kernels, a fairly recent theoretical development that leads to fully smooth subproblems. We first enhance the existing theory to show that our approach is globally convergent in both the primal and dual spaces when applied to convex problems. We then present an extensive computational evaluation using the CUTE test set, showing that some aspects of our approach are promising, but some are not. These conclusions in turn lead to additional computational experiments suggesting where to next focus our theoretical and computational efforts.